Answer:
option B) f(x) = x³ - 3
Step-by-step explanation:
we know that
If the function represent the set of ordered pairs, then the ordered pairs, must be satisfy the function
<u><em>Verify each function</em></u>
case A) f(x) = -2x
verify the ordered pair (2,5)
For x=2
substitute the value of x in the function and then compare the result with the y-coordinate of the ordered pair
![f(2)=-2(2)=-4](https://tex.z-dn.net/?f=f%282%29%3D-2%282%29%3D-4)
![-4\neq 5](https://tex.z-dn.net/?f=-4%5Cneq%205)
the ordered pair not satisfy the function
so
The function nor represent the set of the ordered pairs
case B) f(x) = x³ - 3
Verify (1,-2)
For x=-1 --->
---> is ok
Verify (2,5)
For x=-2 --->
---> is ok
Verify (3,24)
For x=3 --->
---> is ok
Verify (4,61)
For x=4 --->
---> is ok
so
the ordered pairs satisfy the function
therefore
The function represent the set of ordered pairs
case C) f(x) = x² - 3
verify the ordered pair (2,5)
For x=2
substitute the value of x in the function and then compare the result with the y-coordinate of the ordered pair
![f(2)=2^2-3=1](https://tex.z-dn.net/?f=f%282%29%3D2%5E2-3%3D1)
![1\neq 5](https://tex.z-dn.net/?f=1%5Cneq%205)
the ordered pair not satisfy the function
so
The function nor represent the set of the ordered pairs
case D) f(x) = 5x² - 7
verify the ordered pair (2,5)
For x=2
substitute the value of x in the function and then compare the result with the y-coordinate of the ordered pair
![f(2)=5(2)^2-7=13](https://tex.z-dn.net/?f=f%282%29%3D5%282%29%5E2-7%3D13)
![13\neq 5](https://tex.z-dn.net/?f=13%5Cneq%205)
the ordered pair not satisfy the function
so
The function nor represent the set of the ordered pairs